Two circles ω1 and ω2 with radii r1 and r2, r2>r1, are externally tangent. The line t1 is tangent to the circles ω1 and ω2 at points A and D respectively. The parallel line t2 to the line t1 is tangent to the circle ω1 and intersects the circle ω2 at points E and F. The line t3 passing through D intersects the line t2 and the circle ω2 in B and C respectively, both different of E and F respectively. Prove that the circumcircle of the triangle ABC is tangent to the line t1.
Dinu Serbanescu geometrycircumcircleinvariantgeometry proposed